LLMs are a "complicated solution" in the sense that they're expensive. Once you know what they're capable of, you can scale them down to something less expensive. There's usually a way.
Also, an important advantage of LLMs over other approaches is that it's easy to improve them by finding better ways of prompting them. Those prompting strategies can then get hard-coded into the models to make them more efficient. Rinse and repeat. Similarly, you can produce curated data to make them better in certain areas like programming or mathematics.